I don't have any strong feelings for or against the monarchy but one or two thoughts occur. The last time this country tried going without a monarchy it didn't last very long before the restoration took place but perhaps things would be different if we tried again, different folks, different strokes as they say. However, I seem to recall that it wasn't long before Oliver Cromwell was requiring more money from Parliament than Charles I had ever done.
We need a head of state if our version of democracy is to continue. I suspect that an elected head of state would be driven by ambition (even greed) which could place his or her wishes over the best interests of the country. We only have to look at recent revelations about our politicians to see that. S/he could also demand greater powers because of the popular mandate inherent in having been elected. A hereditary monarch can make no such claim.
I don't know much about the way the monarchy is funded but I have a gut feeling that too much money is spent on royals who contribute little or nothing to the country. Where that money comes from I don't know but IMO people like Prince Andrew and Prince Edward really should be earning their own money rather than receiving handouts. Apart from anything else it would set an example which I believe is one of the things we can expect of the royal family (I did say expect, even if we don't get it).